A Simple and Efficient Algorithm for Determining Isomorphism of Planar Triply Connected Graphs

A problem that arises in many practical applications of linear graphs and in some purely mathematical applications is the determination of the isomorphism of two given graphs; such applications include the automatic retrieval of information, machine translation of languages, pipeline and electric networks, pattern recognition, graph-theoretic enumeration problems, the four-color conjecture, and the problem of "squaring the rectangle." Up to the present time only heuristic programs have been developed for solving this problem for general graphs. In this paper, a solution for a class of graphs is given in terms of a simple and computationally efficient algorithm, which is ideally suited for computer programming; a program in MAD language has been written but has not yet been run. The class of graphs considered are planar and triply connected; this class arises, for example, in the four-color problem and in the problem of squaring the rectangle. The algorithm is applicable to both directed and undirected graphs and to simple graphs and multigraphs. The algorithm is based on Trémaux\´s procedure for generating an Euler path in a graph. Application of the algorithm to a plane triply connected graph yields a set of vector codes which are ordered lexicographically in a code matrix.